Basically, you'll need 2 things:
1) a web host that has .Net functionality (which will handle both .ASP and .ASPX files)
2) a database -- preferably SQLServer (since that and ASP are from Microsoft) but Oracle, MySQL or some other database will probably work just fine

I have been using 1and1.com for the past few years without any problems. I recommend their services. They have several levels of service from beginner to advanced. One of those should help you out...